To find the type of triangle, first we determine the length of all the three sides and see whatever condition of triangle is satisfied by these sides.
Now, using distance formula between two points,
AB=√(−4+5)2+(−2−6)2=√(1)2+(−8)2=√1+64=√65 ∵d=√(x2−x1)+(y2−y1)2BC=√(7+4)2+(5+2)2=√(11)2+(7)2=√121+49=√170And CA=√(−5−7)2+(6−5)2=√(−12)2+(1)2√144+1=√145
We see that, AB≠BC≠CA
And Δ ABC do not hold the condition of Pythagoras theorem
i.e., (Hypotenuse)2 = (Base)2 + (Perpendicular)2.
Hence, the required triangle is scalene because all sides are of different length.